Solved Exercises on Standard Form in Grade 1

Master standard form: place value, number representation, and digit identification through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Place value recognition
Exercise 1
Write the number 47 in standard form and identify the place value of each digit.
Show how many tens and ones are in the number 47.
Definition:

Standard form: Writing a number using digits in their correct place value positions

Place value: The value of a digit based on its position in the number (ones, tens, hundreds, etc.)

Place value method:
  1. Identify the position of each digit
  2. Determine how many tens and ones are in the number
  3. Show the expanded form to verify
  4. Write in standard form
4
7
Number
47
Tens
4
Ones
7
Step 1: Identify the digits

In the number 47, there are two digits: 4 and 7

Step 2: Determine place values

The digit 4 is in the tens place, so it represents 4 tens (4 × 10 = 40)

The digit 7 is in the ones place, so it represents 7 ones (7 × 1 = 7)

Step 3: Write the expanded form

47 = 40 + 7 = 4 tens + 7 ones

Step 4: Confirm standard form

The number 47 is already in standard form

47 = 4 tens + 7 ones
Final answer:

Standard form: 47

Digit 4 is in the tens place (represents 40)

Digit 7 is in the ones place (represents 7)

Applied rules:

• Place value: Each position has a specific value (ones, tens, hundreds)

• Standard form: Numbers written using digits in their correct positions

• Expanded form: Shows the value of each digit separately

2 Expanded to standard form
Exercise 2
Convert 3 tens and 8 ones to standard form.
Write the number represented by 3 tens and 8 ones.
Definition:

Expanded form: Showing the value of each digit separately (3 tens + 8 ones)

Standard form: Writing the number using digits (38)

3
8
Expanded
3 tens + 8 ones
Value
30 + 8
Standard
38
Step 1: Calculate the value of tens

3 tens = 3 × 10 = 30

Step 2: Calculate the value of ones

8 ones = 8 × 1 = 8

Step 3: Add the values together

30 + 8 = 38

Step 4: Write in standard form

The number is 38, where 3 is in the tens place and 8 is in the ones place

3 tens + 8 ones = 38
Final answer:

Standard form: 38

This means 3 tens and 8 ones

Applied rules:

• Tens place: Each ten represents 10 units

• Ones place: Each one represents 1 unit

• Standard form: Combine tens and ones to form the complete number

3 Digit identification
Exercise 3
In the number 52, what digit is in the tens place? What digit is in the ones place?
How many tens and how many ones are in 52?
Definition:

Digit: Any of the numerals from 0 to 9

Place value: The position of a digit determines its value

5
2
Tens Place Ones Place
5 2
Number
52
Tens digit
5
Ones digit
2
Step 1: Look at the number 52

The number has two digits: 5 and 2

Step 2: Identify the tens place

The first digit from the left is in the tens place: 5 is in the tens place

Step 3: Identify the ones place

The second digit from the left is in the ones place: 2 is in the ones place

Step 4: Calculate the actual values

5 tens = 5 × 10 = 50

2 ones = 2 × 1 = 2

Total: 50 + 2 = 52

Tens digit: 5, Ones digit: 2
Final answer:

Digit in tens place: 5

Digit in ones place: 2

52 contains 5 tens and 2 ones

Applied rules:

• Rightmost digit: Always in the ones place

• Second from right: Always in the tens place

• Place value: Each position represents a power of 10

Place Value Rules and Methods
23 = 2 tens + 3 ones
Place Value Example
Ones Place
1, 2, 3, 4, 5, 6, 7, 8, 9
Each digit represents 1 unit
Tens Place
10, 20, 30, 40, 50, 60, 70, 80, 90
Each digit represents 10 units
Expanded Form
45 = 40 + 5
Shows value of each digit
Key definitions:

Standard form: Writing numbers using digits (e.g., 47)

Expanded form: Writing numbers showing place value (e.g., 40 + 7)

Place value: The value of a digit based on its position

Place value methodology:
  1. Count positions: Start from the right (ones, tens, hundreds...)
  2. Identify digits: Recognize each digit in its position
  3. Calculate values: Multiply each digit by its place value
  4. Combine: Add all values to get the total number
Tip 1: Remember: Ones place is the rightmost digit.
Tip 2: Tens place is the second digit from the right.
Tip 3: Count tens by 10s: 10, 20, 30, 40...
Tip 4: Always verify by adding expanded parts.
Common errors: Mixing up tens and ones places, forgetting to multiply by place value.
Memory aid: "Tens are groups of 10, ones are individual units."
Place value rules to remember:

• Ones place: rightmost digit, value = digit × 1

• Tens place: second from right, value = digit × 10

• Standard form: number written with digits

• Expanded form: shows addition of place values

Solution: Exercises 4 to 5
4 Standard to expanded form
Exercise 4
Write 64 in expanded form. Then write it back in standard form.
Show the relationship between standard and expanded forms.
Definition:

Expanded form: Writing a number as the sum of its place values

Standard form: Writing a number using digits

6
4
Standard
64
Expanded
60 + 4
Place value
6 tens + 4 ones
Step 1: Identify each digit's place

6 is in the tens place (represents 60)

4 is in the ones place (represents 4)

Step 2: Write expanded form

64 = 60 + 4 (expanded form)

Or 64 = 6 tens + 4 ones

Step 3: Verify by adding

60 + 4 = 64 ✓

Step 4: Return to standard form

When we combine 60 and 4, we get 64 in standard form

64 = 60 + 4 = 6 tens + 4 ones
Final answer:

Standard form: 64

Expanded form: 60 + 4 or 6 tens + 4 ones

Applied rules:

• Expanded form: Separate each place value and add them

• Standard form: Combine place values into a single number

• Verification: Adding expanded parts should equal standard form

5 Word problems to standard form
Exercise 5
Sarah has 2 tens of pencils and 9 ones of pencils. How many pencils does Sarah have in total? Write the answer in standard form.
Definition:

Word problems: Real-world scenarios requiring mathematical solutions

Standard form: Final answer written with digits

2
9
Given
2 tens + 9 ones
Calculate
20 + 9
Total
29
Step 1: Understand the problem

Sarah has 2 tens of pencils = 2 × 10 = 20 pencils

Sarah has 9 ones of pencils = 9 × 1 = 9 pencils

Step 2: Add the quantities

Total pencils = 20 + 9 = 29 pencils

Step 3: Write in standard form

The number 29 is in standard form

Step 4: Verify the answer

29 = 20 + 9 = 2 tens + 9 ones ✓

Sarah has 29 pencils
Final answer:

Sarah has 29 pencils in total.

Standard form: 29

Applied rules:

• Word problems: Identify key information and convert to math

• Place value: Tens represent groups of 10, ones represent singles

• Standard form: Write final answer using digits

Place Value Laws, Methods, and Key Concepts
37 = 30 + 7 = 3 tens + 7 ones
Standard vs Expanded Form
Key definitions:

Standard form: A number written using digits (e.g., 54)

Expanded form: A number written as the sum of its place values (e.g., 50 + 4)

Place value: The value of a digit based on its position in the number

Digit: Any numeral from 0 to 9

Ones place: Rightmost position, value = digit × 1

Tens place: Second position from right, value = digit × 10

Complete methodology:
  1. Identify the number: Look at the given number or word problem
  2. Determine place values: Identify which digits are in tens and ones places
  3. Calculate values: Multiply each digit by its place value (10 for tens, 1 for ones)
  4. Convert forms: Switch between standard and expanded forms as needed
  5. Verify: Check that expanded form adds up to standard form
Tip 1: Always start counting place values from the right side.
Tip 2: Draw place value blocks to visualize numbers.
Tip 3: Practice saying numbers aloud: "twenty-three" means 2 tens and 3 ones.
Tip 4: Use base-10 blocks or drawings to represent numbers concretely.
Tip 5: Check your work by adding expanded parts to make sure they equal the original number.
Common errors: Reversing tens and ones places, forgetting to multiply by place value, misreading word problems.
Memory aids: "Tens are bigger groups (10 each), ones are single units (1 each)."
Visual strategy: Draw lines under each digit and label tens and ones above them.
Place value laws and formulas:

• Standard form: n = tens digit × 10 + ones digit × 1

• Expanded form: tens digit × 10 + ones digit × 1

• Place value pattern: ones, tens, hundreds (each place is 10× the previous)

• Digit value = digit × place value

• Verification: expanded form should sum to standard form

Questions & Answers

Question: I don't understand why 23 is different from 32. They have the same digits, don't they?

Answer: Great observation! Yes, both numbers have the same digits (2 and 3), but their positions make them completely different:

  • In 23: The 2 is in the tens place (represents 20) and the 3 is in the ones place (represents 3)
  • In 32: The 3 is in the tens place (represents 30) and the 2 is in the ones place (represents 2)

So: 23 = 20 + 3 = 23, while 32 = 30 + 2 = 32

Think of it like money: having 2 ten-dollar bills and 3 one-dollar bills ($23) is different from having 3 ten-dollar bills and 2 one-dollar bills ($32).

The position of each digit determines its value - this is called "place value!"

Question: My child is struggling with expanded form. How can I help them understand that 45 equals 40 + 5?

Answer: Here are effective strategies to help your child understand expanded form:

  • Use physical objects: Give them 4 bundles of 10 straws (or toothpicks) and 5 single straws
  • Draw pictures: Draw 4 groups of 10 circles and 5 single circles
  • Count together: Count the tens first (10, 20, 30, 40) then count the ones (41, 42, 43, 44, 45)
  • Connect to words: Say "forty-five" as "four tens and five ones"

Practice with many examples: 27 = 20 + 7, 63 = 60 + 3, 89 = 80 + 9

The key is helping them see that the first digit tells us how many groups of 10, and the second digit tells us how many extra ones.

Question: Why do we need to learn standard form? Can't we just count everything?

Answer: Great question! We learn standard form because it helps us:

  • Write numbers quickly: Instead of drawing 23 dots, we write "23"
  • Understand big numbers: It's much easier to write "100" than draw 100 dots
  • Do math operations: Addition and subtraction are much faster with standard form
  • Communicate numbers: Everyone understands what "45" means instantly

Think of standard form like a shortcut - it's a quick way to write how many things we have without having to draw or count each one individually!

As you get older, you'll use standard form for bigger numbers like 100, 1,000, and even millions!